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Register a new userTest of Einstein-Podolsky-Rosen Steering Based on the All-Versus-Nothing Proof
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In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosen steering is a newly emerged research topic and in its incipient stage. Although Einstein-Podolsky-Rosen steering has been explored via violations of steering inequalities both theoretically and experimentally, the known inequalities in the literatures are far from well-developed. As a result, it is not yet possible to observe Einstein-Podolsky-Rosen steering for some steerable mixed states. Recently, a simple approach was presented to identify Einstein-Podolsky-Rosen steering based on all-versus-nothing argument, offering a strong condition to witness the steerability of a family of two-qubit (pure or mixed) entangled states. In this work, we show that the all-versus-nothing proof of Einstein-Podolsky-Rosen steering can be tested by measuring the projective probabilities. Through the bound of probabilities imposed by local-hidden-state model, the proposed test shows that steering can be detected by the all-versus-nothing argument experimentally even in the presence of imprecision and errors. Our test can be implemented in many physical systems and we discuss the possible realizations of our scheme with non-Abelian anyons and trapped ions.
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Einstein-Podolsky-Rosen (EPR) steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It allows for entanglement certification when the measurements performed by one of the parties are not characterised (or are untrusted) and has applications in quantum key distribution. Despite its foundational and applied importance, EPR steering lacks a quantitative assessment. Here we propose a way of quantifying this phenomenon and use it to study the steerability of several quantum states. In particular we show that every pure entangled state is maximally steerable, the projector onto the anti-symmetric subspace is maximally steerable for all dimensions, we provide a new example of one-way steering, and give strong support that states with positive-partial-transposition are not steerable.
We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range for two qubit Werner states in the two measurement and two outcome scenario. We further employ the derived steering relation for several classes of continuous variable systems. We show that non-Gaussian entangled states such as the photon subtracted squeezed vacuum state and the two-dimensional harmonic oscillator state furnish greater violation of the sum steering relation compared to the Reid criterion as well as the entropic steering criterion. The sum steering inequality provides a tighter steering condition to reveal the steerability of continuous variable states.
Protocols for testing or exploiting quantum correlations-such as entanglement, Bell nonlocality, and Einstein-Podolsky-Rosen steering- generally assume a common reference frame between two parties. Establishing such a frame is resource-intensive, and can be technically demanding for distant parties. While Bell nonlocality can be demonstrated with high probability for a large class of two-qubit entangled states when the parties have one or no shared reference direction, the degree of observed nonlocality is measurement-orientation dependent and can be arbitrarily small. In contrast, we theoretically prove that steering can be demonstrated with 100% probability, for a larger class of states, in a rotationally-invariant manner, and experimentally demonstrate rotationally-invariant steering in a variety of cases. We also show, by comparing with the steering inequality of Cavalcanti et al. [J. Opt. Soc. Am. B 32, A74 (2015)], that the steering inequality we derive is the optimal rotationally invariant one for the case of two settings per side and two-qubit states having maximally mixed reduced (local) states.
If entanglement could be verified without any trust in the devices of observers, i.e., in a device-independent (DI) way, then unconditional security can be guaranteed for various quantum information tasks. In this work, we propose an experimental-friendly DI protocol to certify the presence of entanglement, based on Einstein-Podolsky-Rosen (EPR) steering. We first establish the DI verification framework, relying on the measurement-device-independent technique and self-testing, and show it is able to verify all EPR-steerable states. In the context of three-measurement settings as per party, it is found to be noise robustness towards inefficient measurements and imperfect self-testing. Finally, a four-photon experiment is implemented to device-independently verify EPR-steering even for Bell local states. Our work paves the way for realistic implementations of secure quantum information tasks.
The Einstein-Podolsky-Rosen (EPR) steering, which is regarded as a category of quantum nonlocal correlations, owns the asymmetric property in contrast with the entanglement and the Bell nonlocality. For the multipartite EPR steering, monogamy, which limits the two observers to steer the third one simultaneously, emerges as an essential property. However, more configurations of shareability relations in the reduced subsystem which are beyond the monogamy could be observed by increasing the numbers of measurement setting, in which the experimental verification is still absent. Here, in an optical experiment, we provide a proof-of-principle demonstration of shareability of the EPR steering without constraint of monogamy in the three-qubit system, in which Alice could be steered by Bob and Charlie simultaneously. Moreover, based on the reduced bipartite EPR steering detection, we verify the genuine three-qubit entanglement. This work provides a basis for an improved understanding of the multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection and quantum cryptography.
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